Planimeter



2 Sheets-Sheet 2 Armmwsx P. E. LEH R PLANIMETEIR Jan. 3, 1933.

Filed April 25, 1930 Patented Jan; 3, 1933 UNITED STATES PAUL E. LEER, OF OILFIELDS, CALIFORNIA PLANIMETER Application filed April 23,

My invention relates to planimeters, and more particularly 120 an averaging planimeter of the radial type such as is used 0n circular charts for determining the average raclius of a eurve cl1awn thereon.

It is often desirable to be able t0 record values of a variable such as temperature, pressure, liquid-level, etc. 0ver a period of time so that a permanent record of instantaneous values may be kept. This is usually done by rotating a chart as a function of time and drawing a eurve thereon as a function of the variable which is 130 be recordecl, the radial distance from a given zero line on the chart representing the value of the variable at any instant of time.

In certain instances it is desirable to be able 170 cletermine the average reacling of such a chart over a given period of time, this periocl usually being a twenty-four hour one representecl by a full revolution of the chart. Various devices have been designed t0 accomplish this end, all of which are expensive 130 manufacturedue 130 ehe necessity o-f providing aceurately graduated scales and verniers. F urther it has heretofore been necessary to use transformationcharts or factors to interpret the reading 01 the instrument scales in tenns of the variable recorclecl on the chart. In orcler t0 obtain direet readings it has heretofore been necessary to design an instrument for use with a single type 0f chart.

It is a piimary object of this invention to provide an averaging planimeter which itself earries no gracluatecl seale requiring the use of transformation eharts 01' factors, but Which insteacl giv(es a clirect reading of the clesired ave1age by utilizing the calibrations 0n the chart itself.

A further object of the invention is to provide such an instrum'ent which is much simpler to construct ancl use than are exis'ting in- 1930. Serial N0. 446,619.

indicating relationship Wih the calibrations of the chart. A planimeter wheel contacts the chart and is turnecl by a relative movement between the chart ancl this wheel, the inclicator being movecl as a function of the angular movenient 0f the planimeter wheel. In acldition, the perferrecl form carries a pointer means which is macle 150 follow the curve on the chart.

It is an important object of this invention t0 provide an averaging plani1necer of this type in whieh ehe point 0f contact between the planimeter wheel anal chart lies 0n a raclius which passes through the poincer 1neans ancl which is clrawn through the center 0f the chara.

A further obj ect 0ii the invention is t0 provide such a plani1neter in Which the pointer means is spacecl a given distance frorn the planimecer wheel and in which a reference 7G means is utilizecl to preliminarily cletermine the starting position of the inclicator, this reference means being spacecl from the center 0f the chart a distance equal t0 said given clistanee.

A. further object of the invention is t0 provicle a planimeter inclucling a planimeter vvheel engaging the upper surface 0f a chart clirectly above a shallow channel formecl in the base member which supporcs the chart.

Still a fu1ther object of ehe invention is to provicle a planirneter applicable so any circular ehart Which is uniformly gracluatecl. It is also possible to aclapt the planimeter of my invention to other types 0f charts Which are not unifonnly gracluatecl by suitably designing the screw which interconnects the pointer und the planimeter wheel.

A further obj ect of the invention is 110 provicle a planimeter in which the chart is rotated relative to the planimeter mechanism rather than moving this meehanism relative to the chart, the former system being preferable clue 130 ehe lack of inertia forces Which must be overco1ne in making the poincer follow the curve.

Further objects lie in the specific construction 0f the instrument and Will be made evident hereinafter.

Referring to the drawings, 111 which I have illustrated a preferred forrn,

Fig. 1 is an isometric View of my planimeter showing the mechanism in starting positiln.

F ig. 2 is 21 sectional view taken 011 the line 22 01 Fig. 1.

Fig. 3 is a sectional view taken 011 the l111e 33 of Fig. 2.

Referring these drawingzs, the averaging planimeter of my invention includes 21 base 10 providing rubber posts 11 which sup port th'e base 10 21 distance above the surface 12 011 which the planimeter rests. For111ed in the upper surface of this base is 21 shallow cha1nnel 15 best shown in Figs. 1 a11d 3, z1nd the mat=erial remz1ining 111 the bottom of this channel is cut z1way t0 form 2111 elongz1ted 0 je11111g 16 01 uniform width and extendling th'rough a suhstantialportion of tl1e l ength of the channel 15. 1

' .Adapt ed 10 slide along tl1is elongga.ted Opening is a chart holder 18 providing 21 flat h021d 19 positioned in the chanriel 15 :md extending 21 slight distflnce above the upp0r :Ee1ce of the base 10. -This chartholder 18 also provides 21 shank 20 Which extends through tl1e open- -ing16 2111d whichis threaded 'at 115 lower end to receiv0 alle shank o1 21 screw 22. A washer 23 ispo'sitioneol between the head 01 th'e sorew 22 2111d the lower surface of the base 10, tl'1is Washer being of such 21 thickness thz1t the hart holder 18 slides freelf; along ehe elongated opening 16., 5

" Adapted to loe positi0ned on the chart holder 18 is a chart 25 of the circular type, th'1s chart including 21 central opening which sn'ugly fits overthe head 19 of the chart holder 18; thus alloWing the ehart t0 be turned 211'011nd the verticel axis of this 0h21rt holder, and also to loe moved in 21 direction parallel 10 the axisof the el'ongated opening 16. This chart-1s 01: ehe, conventional type profvidi ng calilorations 26 which, in the form shown, 'cornp1se -equally spaced graduation lines 27 which are cor1centric with each other the innermost 0f these grad1'1ation lines for1hing 11 zero line indioated loy the nurneral 28. 111- c0rSecting thegraduat ion lines 27 are ahneindiez1ting lines 29 which, 111 th e forn1 shoWn, &re formed 011 the arc of 21 circle due 10 the constructio'n of the instrument Which is uSed -for drawing 21 curve 0n t-l'1is chart. Th11s, 11 a curve of pressure agz1inst time is desired, the pointer drawing the r:urve n1oves through the arc of a'C1rcle corresponding in curvature to the tim1'edndicating lir1es 29, and if the Chart 25 is driven by suitaloly tin1ed mechanism, 21- curve 30 is drawn 011 the chart. From a'n inspection of such 21 eurve it is p0ssihle to determir1e the Value 01E the .pressure 2113 a11y A supporting arm 32 is mounted in spa0ed .relationship Wih the 11pper surfaceo1 the base 10 by any suitable means. In Fig. 1 this rneans is shown 215 con1'prising 21sp2100r 33 a p1n 39 mounced 111 thesupportinp; arm 32 21r1d extending inwz1rd fromm the vertical faces 35 and 30. The p111 011 the free 011d of the supporting ar1nis preferaloly so formed as 10 be easily 1e11101 '21l0le 10 pern1it oho fran1e 10 be easily Securedin place. ;This frz1me38 is 01: such a lengt-h es tosubstantially fill the c'ut-a'w21y portion between the vertiealfaces 35 2111d 36 so that 110 n1oven1ent of;this frame z1long the arm 32 02111 hake place. v

Formedon 0I1positeends of the fran1e 38 z1re arms40 a11d41 which extend over the shallow channel 15, the free ends of these arme oarrying pins 43 whieh 21re easily, re{ movable theirofrom, these pins be1ngr, of such 21 length 21s to extend inward from the arme 2111d provide a 1oivot means for a threaded shaft 415 ext-endinp; therebetween. Tl1e 21x1s of this threz1ded shaft liesd irectlyabove the &X1S 0f the' eher; holder 182111dlies parallel to the 21X1s 01 the elongated opening 16. 21nd the threa'ds 'formed thereon hz 1ve- 21 relatively steep pitch. as Will loe hereinafter explzrined. these' threads being indicated b y oho nu111 eral 4621nd in sl1e preferred fo-rgm taking the form 01 21 helical groove cut in the shaft45.

Thz1t 011d -0f the threaded sl121'ft45 whi0h is pivoted 111 the arm 40-'carries 21 planimeter wheel 50 WhiCh is s11itably securedo the shaft in 21 plane perpendicular 150 the axis there of.

Also secured 10 the arm 40 is 11 pointermeans 52 cornprising an arm 53 extending forward and being bent eo errtendz1c-ross the front of the planimeter wheel 50, the free vend the10of beinghenb t o extend 111W21rd1111d downward 10 f0 rrn a pojnter 54 which lies close 10 the calibrations of'the cl1a rt 25. In the pre ferred emloodiment of m v invention I. so'position the pointer 54 th21t the tip thereof lies 011 z1radius drawn from the vertical axis of the eher tween the chz1rt und the 13l21111111et0r wheel 50. Threaded on, the shaf't 45 .1's an indicz'1tor in/a0 close 111011111111V100h0 upper surface of hoWever, made ofs11ch 21 length -tl1afifielea1rs t holder 18 through the p'oint -of eonrac be- 60 providing 21 noint 61 eXtendihg d0wnWard the head 19 0'f the hart holder l 8loy 21 small margin vvhen' ehe Shaft 45 is r0tated. Tl1is 1'11 dicacor c21rries an arm 62 Whi0l1 ext011dsre211- Y v ward z1nd which is bi'furca1ed 10 p'rovide extens1ons63 and 61flying respectively above hn d belowjche frz1me 38 so as to beslideble 13 therealrng. The arm 62 prevenos any rotetion of the indicator on the shaft 45.

The instrument thus described is 01 the radially ofi-set type, this term not being restricted to the sense sometimes used with such instrumencs wherein the planirneter wheel 50 is radially disaligned from the pointer 54, but l3811'1g used in the sense that the planimeter Wheel 50 is spaced from the pointer 54 in a radial direction. When this form of instrument is used, it is necessary to provide 21 reference means adja.cent whieh, point 61 of the indicator is positioned before rotating the chart to determine Ehe average radius of bhe curve 30 thereon. This reference means must be somehow assoeiated with the axis of the chart and in the preferred form ehe periphery of the head 19 of the chart holder 18 is used for this purpose. Thus, in 1 I have shown the point 61 as lying directly ahove ehe periphery of the chart holder 18. this he 'ng the correct starting position for the instrument shown. Itshould not be understood, however, that I am limited to the uee of the periphery of the chart holder es co-nstituting this reference means. It is also possible to inscribe a circle on the chart holder 18 which may be used for a reference means. It is important to note however, that the distance between the vertical axis 0f the chart holder 18 and the reference means utilized should be equal to the radial distanee hetween the pointer 54 and the point of contac between the planimeter Wheel 50 and the chart 25.

It should not be inferred, however, that I am limited to this radial off-set system. In some instances it is possible 150 use the planimeter wheel 50 as a pointer means for following the eurve 30. In such a system the dis tance between the pointer means and ehe point of contact of the planimeter Wheel 50 and chart 25 would, of course, be equal to zero,

' and the reference means would thus correspond to the vertical axis of the chart holder 18.

In the operation of the form shown in Fig. 1, an arbitrary starting point lying on the curve 30 is suitably marked and brought under the pointer 54. It is usually preierable Wih the form of instrument herein deseribed in detail to seleet the point 70 ab er near die maximum value of the curve 30. The forward end of bhe frame 38 is then momentarily lifted und the sha:ft 45 rotated until the point 61 of the indicator 60 lies above the reference means, in the forme shown this reference means being the periphery of the chart holder 18. The fra.me 38 is thei1 lowered. and the mechanism is in the starting position shown in Fig. 1. The operator rotat es the chart- 25 in a direotion indieated by Ehe arrow 71 of Fig'. l, this being done hy manual engagemen't, With the ehart. By moving the chart to theright or to the left during this rotation it is possible t0 make t-he pointer 54 follow the curve 30. After the complete curve has been traced and ehe pointer 54 again lies directly above the starting point 70 previously indi ceted on the eurve 30, the operator notes the position of th e pointer 61 with relation to the graduation lines 27. It Will be found that if the threaded shaft 45 is suitably designed with relation to t-he diameter of the planimet-er wheel 50, the point 61 Will lie directly above that graduation line representing the average value of the curve 30.

The theoretical considerations involved in the design of my planimeter are quite simple, and the equat-ions for designing an instrumenu which is 11015 radially oiI-set Will be given. Thus, assuming (hat the planimeter Wheel 50 is to be the pointer means, and assuming for the purpose of simplicity that the Wheel is to follow a circle the radius of which is represented by R, this radius being haken with respect 1 0 the vertieal axis of the chart holder 18, and assuming the diameter of the planimeter wheel t0 'oe represented by a. value D, it follows that if the planimeter wheel is run around the circle 0f ehe radius R, Ehe revolutions of this planimeter Wheel would be equal to Inasmuch as we desire the indioator 60 t0 mov e a distance R, and inasmuch as this dis ance is direetly proportional to N, the number of revolutions of the planimeter wheel, and inversely proportional 150 X, which is the number o1 threads per inoh 011 the serew 45, it follows that Substituting th e seeond equation in the first, we obtain It is important to note that the variables D and X are independent of the nun1ber 01 revolutions, thus making 116 possible t0 use my in strument on all charts having uniformly spaoed graduation lines, regardless of the values attaehed thereto. F ron1 the ahove equation it Will he readily seen that if the planim ter wheel is so for1ned es 120 have 21 diameter of one inch, the number of threads per inch whieh must be formed 011 the threadrevolutions.

'ed shaft 45 is equal to 2.

These equations irre equally applieahle to a planimeter of the elf-sei: type such es shown in Fig. 1 if it .is remembered thal: the distance between ehe axis of the chart and holder 18 and the reference means is equal to the dis tance bet-ween the pointer 54 and the point 0f contaet of the planimeter wheel 50. Iv; is 0bviously preferable in most cases to use die ofiset type inasmuch as the pointer means may be spaced from the planimeter wheel 50 tl1ns giving an operator a clear view of this po1nter means and tending to make possible 'a more acourate following of the curve 30.

It should beunderstood that I am not limited to a reference means formed 011 tl1e clnart holder 18; ohisl referen ce means might be 011 the chart itself 01, in fact, might b indicated by a scrateh on tho frame 38, with sonne portion of ehe arm 62 being brought adjacent this scratch to bring the indicator 60 into its starting psition. j

Furthermore, my invention i s not hnnted to an instrurhent wher-ein the indicator 60 moves 120 the right during the time tl1at; the pointer rne ansig following tl1e curv e 30. By reversing the threads 46 011 the threadedshaft 45 it is po5sibleto make this indicator move -leftward 2 md indicate diam-etrically opposite fro'm tl1e pointer 1neans 52.

An importa=nt feature of the invention l1es in the forming of the shalloW channel 15 in the base 10 so that the vveight supported by the planimeter wheel 50 slightly depresses the chart 25 into this channel, thug giving more surfaoe of contact between alle planimeter wheel an d the upper surface of the chart 25. It is, however, desirable not to make this surface of contact to0 large for otherwise the accuraoy of the instrument might be impaired.

I claim ns my invontion:

l. In coxnbination'in a planimeter adapted deterinine the average valuo of a curve d1awn on a oircular ohart: a base adapted t0 hold said chart; an indicator movably mounted relative to said base and positioned a short distance fro1n said chart in a manner to movo over the calibrations thereon in indicating relationship pointer rneans extending adjacent said Chart; and n1eans drivaloly Connected to said indicator and adapted loy engagen1eno with said chart for moving said indicator relative to said calilorations when a relative move1nent between said chart and said'pointer mearis is oflected so that said indicmtor const'antly indicates upon said chart tl1e average value of tl1e ourve tracod by said ointen means.

2. In combination in a planimeter adapted to d termine tl1e avierage Value of a ourve dmwh 011 a Circular Chart: a base adapted to l1 old said chart an indicator movably mounted relative t0 said bas o andpos itionod a short dlstance from Said chart in a manner to rnove over tho calibrations theroon in indicatirig rolntionship; pointer means extending adjacent said Chart; a planimeter wne9l contaoting sn-id chart and rotaoed when a relative moven 1ontbtWeen said cl1art and said point- @1 1nenhs tal es place; and drive means operntiv@ly connecting said indicator and said planimeter wheel to 1nove said indicator as a funotion 01'. the' amount ol:' movomont of Said planimoter Whoel so tl1at said indicator -pointer means takes place, tl1o point of Contact between said planimeter wheel and said Chart be1ng radmlly al1gned W1bh sa1d po1nter means'; and drive1neans operatively conn-ectin g said indlcator and said plani1neter wheel t0 1nove said indicator as a function of the annount of 1novement of said pla1'1in1eter wheel.

4-. In combination in a-planixnete'r ada'pted to detennine the averag e value of a curve drawn on a circular chart: abase adaptod t0 hold said ahmt; an indioator m0vably mounted Motive to said base and positioned a short distance froln said charo in a 1 nannerto 1nove vor the caliloraions thereon in 'indicating r-elationship; pointer mans extending adja-- cent said chart; a planimeter wheel cont'acting said hart and rotat-ed when a relative 1novement betwoon said chart and said pointer means talies place; 1"eference m oans associated with said chart adjacent which said indicator is positioned als starting'to determine the aver'age value 01"? Said curve; and drive meansoperati'vely connecting said indi'ca'tor and said planimeter wheel to move said indicator as a funotion o f the a'mount of mo've-' men of said planin1eter wheel.

5. In co1nbination in a planimeter adapted to determine the zwerage value of a cu rve drawn o-n a circular chart a, base adapted 130 hold said chart; an indicator movably mounted relative co said baso and positioned asl1ort distanoe fron1 said chart in a man1ier to move over tho calibratiorw 'thereon in indicating relationship; pointer means extending adjacenu said Chart; a planimeter wheel contacting s2tid cl1art and.rt liated when a relative 1novement between said charo and said pointer 1noms taks plane, Said Polriter means being spaced a given distance Qt'r01n the point of contact witl1 said planimeter wheel and said chart; refefence means associated with said chart und spaced from the Cenzer thereof a dmtance equal to s2ud g1ven distance, sadd roference 1neans being tl1o starti ng point f01' t l1e travel of sa1d 1nd1cator; and drive n1ezu1s operat1vel; connectmg sznd indicaor und said planime ter wheel to m0ve said indicatr as a functi0n of ehe amount df movement of said plani1neten wheel.

6. Incombination in a pla'nimo-ter aLdapted to determine the aver2ige value 0f a curve drawn on a circular ohart: a chart-holding means; a planimeter wheel contaeting said chart and adapted to be turned by a relative move1nent 0f said chart and said planimeter wheel; pointing n1eans radially spaeed fro1n the point of contact of said chart and seid planimeter wheel; an indicating 1neans independent of said planimeter vvheel; and con necting means so associating said indicating means and seid plani1neter wheel that said in dicating means is moved 21s 21 function of the amount of rotation of said planimeter 1vheel.

7. In combination in a planimeter adapted t0 determine the average value 0'f a curve drawn on a circular chart: a base adapted to hold said chart; a shallovv channel formed in said base; 21 fra1ne mounted above said chart; and a planimeter vvheel rotatably 1nounted in said frame and contaoting said ohart at a point above said cl1annel vvhereby said chart is depressed sligl1tly.

8. A combination as defined in clai1n 7 in which an opening is forn1ed in the botton1 oi' said channel and including a chart holder slidable in said opening along said channel.

9. In combination in a planimeter adapted to determine tl1e average value of a curve drawn on 21 ciroular cl1art: a base; a ohart holder slidable relative t0 said base; a threaded shaft rotatably mounted above said chart; an indicator threaded 011 said shaft and extending adjacent calibrations on said chart in indioating relationship; and a planin1eter wheel drivably connected to said threaded shaft.

10. In combination in a planimeter adap ed to determine tl1e average value of a curve drawn on 21 circular chart: a base; a chart holder slidalole relative to said base; a threaded shaft rotatably mounted above said ehart; an indicator threaded on said sl1aft and extending adjacent calibrations 011 said chart in indicating relationship; a planimeter wheel drivably connected t0 seid threaded shaft; a pointer means adjacent said cl1art and spaced 'fro1n said planimeter wheel a given distance;

and reference n1eans carried by said cl1art holder and spaced frorn the center thereof a distance equal to said given distance.

11. In combination in 21 planirneter adapted to determine tl1e average value of a curve drawn 011 a ciroular chart: a base; a supporting arm mounted on said base but spaced a distance therefrom for a portion of its length to provicle a space into Whiol1 seid ehart may extend; 21 fran1e mounted in seid supporting arm; a threaded shai't pivoted in said frame; a planimeter vvheel seoured 150 said shaft and contacting seid chart; and an indioator threaded on said shaft and movable therealong when 21 relative movernent between said chart and said planirneter Wheel takes place, seid indicator extending close to said ehart in indioating relationship with the calibrations thereon.

12. In con1bination in a planimeter adapt ed to determine tl1e average value of a ourve drawn on a eircular ehart: a base; a supporting arm mounted 011 said base but spaced a. distanee therefrorn for a portion of its length to provide a space into which said cl1art may xtend; a irarne n1ounted in said supporting arm; a threaded shaft pivoted in said frame; a planizneter wheel secured t0 said sl1aft and Contacting said cl1art an indicator threaded 011 said sl1aft anal movable therealong when a relative rnove1nent between said chart and said planimeter wheel takes place, sa 'd indicator extending close to said chart In indieating reletionship with the calibrations tl1ereon; and an arm 011 said indicator and slidable along seid frame to prevent any rotation of seid indicator about the axis 0f seid sl1aitt.

13. In cornbination in a planimeter adapted to determine the average value of a curve drewn 011 a eircular chart: a base; 21 supporting arm mounted on seid base but spaced a distanee therefron1 i'or a portion of its length to provide 21 spaee into which said ohart may extend; a frame pivotally mounted in said supporting arm; a threaded shaft pivoted in said frame; a planimeter Wheel secured t0 said shaft and contacting said chart; and an indicator threaded 011 said sliaft and movable therealong when a relative movement between said chart and said planimeter wheel takes place, said indioator extending olose to said cl1art in indicating relationship with the calibrations thereon.

' '14. In oombination in a planimeter adapted to determine tl1e average value of a curve drawn 011 a chart: supporting means for said chart; an indieating member movably mounted relative to said supporting means andin indicating relationship 1vith calilorations on said chart; and means actuated by the relative movement between said chart and said supporting means for moving said indieating 111e1nber to oontinuously indicate directly upon said ol1art the average value of said curve during said relative movernent. 15. In con1bination in a planimeter adapted to determine the average value of a curve drawn on a chart: supporting 1neans adapted forsupporting said chart, said chart being rotatable andn1ovable in a predetermined patl1 relative to said supporting means so that point fixed relative to said supporting ineans 11121y trace said curve; an indicating 1nernber movably mounted relative to saicl supporting 111e21ns and in indicating relationsl1ip with calibrations 011 said Chart; and means actuated by tl1e relative 1novement of s2iid chart and said supporting means for moving said indicating 111e111ber to indicate upon said"calibrations said average value.

16. In combination in a planimeter adaptedto determine the average value of a e1iive drawn on a chart: supPorting means adapt edfr supporting said chart, said chart being rotatable and movable in a p'redetermined path relative to said Supporting means so thata point fixed relative tosaid supporting means may trace said c-urve; a supporting T member parallel to said path; an indicating n1efmbermovaloly associated with said supwith calib'rations 0n said chart; and .drive Ineans actuated by the relative mo'vement of said Chart and said supporting means for movi'ng said indicating 1nember relative to said Supporting me1nber t0 indicate said a'Verage value upon said calibrations.

17. In Combination in a planimeter adapted to determine the average value of a-curve drawn on a chart: a base providing a shallw Channel; a chart holder slidable relative t0 said base; a threaded shaft rotatably mounted adjaCent said Chart; an indicator threaded on said shaft and extending adjacent calibrations on said chart in indieating relationship; a Planimeter wheel drivably c0nnedted to said threaded shaft and nontatzting said chart above Said channel Whereby -said chartis depressed slightly; a pointer m'eans adjacent said chart and spaced from said .planimeter wheel a given radial distance; and reference 1neans defining a start i1'1g point f0r said indicacorand spaced from the Center of said chart a distance equal to Said given radial distance.

v 18. In combination in a planimeter adapted to determine the average value of a cnrve 0n a circular chart: a base adapted to hold said chart; a shallow channel formed in said base; a fra1ne mounted adjacent said chart;

a planimeter Wl1eel rotatably 1nounted in said fran1e and contacting said Chart at a point above said channel Whereby said chart is depressed slightly; and reierence 'means adjacent said ehart for indicating the positin of-said indicator before starting to determine the average Val11eof said curves.

" 19. In combination in a planimeter adapt" ed to determine the average Value of a eurve drawn on a chart: a base providing a shal- 10W channel; a chart holder slidable relative to saidbase and adapted :Eor rtatably supporting said chart; a threaded shaft rotatably mounted adj acent said chart; an indicatdr threaded on said shaft and extending adjzicent calibrations on said chart in indi. cating relationship; a planimeter wheel drivably connected to said threaded shaft and c0ntacting Said chart above said channel whereby said chart is depressed slightly 'and a pointer means adjacent said chart.

In testimony whereof, I have hereunto set my band at Los Angeles, California, this 19th day 0f April, 1980.

" PAUL E. LEER.

portirig member in indicating relationship 

